1. Field of the Invention
The present invention relates generally to measuring the relative displacement between two entities (such as satellites, airplanes, etc.) or between any moving or static entities, wherein such displacement is measured in three (3) dimensions.
2. Description of the Related Art
(Note: This application references a number of different publications as indicated throughout the specification by reference numbers enclosed in brackets, e.g., [x]. A list of these different publications ordered according to these reference numbers can be found below in the section entitled “References.” Each of these publications is incorporated by reference herein.)
The measurement and study of variations in the acceleration caused by gravity is called gravity gradiometry. This technique has been used to examine subsurface geology to aid hydrocarbon (oil), water, mineral exploration, tunnel and bunker detection. The most frequently used and intuitive component is the vertical gravity gradient, Gyy, which represents the rate of change of vertical gravity (gy) with height (y). As an example, a person walking past at a distance of two (2) meters would provide a gravity gradient signal approximately equivalent to 10−9 m/s2 [3].
Recently, the Gravity Recovery and Climate Experiment (GRACE) (which was a joint mission of NASA and the German Aerospace Center) and the Gravity Recovery and Interior Laboratory (GRAIL) mission (which is part of NASA's Discovery Program) have used a gravity gradiometry technique for mapping the gravitational field of the Earth and the Moon, respectively. Both missions are very similar to each other; they are composed of two twin satellites following each other in the same orbit, [1,2]. As the first satellite passes over a region of stronger gravity called a gravity anomaly, it is pulled ahead of the trailing satellite. This increases the separation distance between the two satellites. As the first satellite moves away from the anomaly, it decelerates; meanwhile the second satellite approaches the anomaly, therefore it accelerates. The combination of these two phenomena induces a decrease in the relative distance between the two satellites. By constantly monitoring the relative distance between the two satellites, scientists are able to construct a detailed map of Earth's and Moon's gravity.
One can notice that the major instruments of these techniques are the ranging system called the Lunar Gravity Ranging System (LGRS) in the case of GRAIL and High Accuracy Inter-satellite Ranging System (HAIRS) in the case of GRACE. The LGRS and HAIRS measure the relative displacement of the two satellites along the path way, which is almost the orbit of the two satellites referred to as z. The ranging system, which is the heart of the current satellite gravity gradiometer technique, is based on the Doppler Effect, which measures the phase change of a wave travelling from one satellite to the other to determine the change of the relative distance between the two satellites. However, such a ranging system only measures the distance along the axis of propagation of the E&M (electromagnetic) field, while not making any measurement on the two other perpendicular directions, thus being unable to construct a full tensor gradiometer. It is noteworthy to observe that the most frequently used and intuitive component of the gravity field is the vertical gravity gradient, which for a circular orbit is perpendicular to the direction of propagation of the two satellites. Indeed, the orbit of the satellites is assumed to be a surface of constant gravity potential U and let r1 and r2 be positions on the surface (i.e., with U1 and U2=U), then the component of g along the axis of the orbit is zero.
The g=−grad·U has no components along the axis of the orbit. This illustrates how important is it to measure the relative displacement of the two satellites in the plane horizontal to the axis separating the two satellites, which the currently technology based on the Doppler technique doesn't address.
Accordingly, what is needed is the ability to accurately (e.g., without a significant impact due to noise) measure the relative displacement between two satellites in three (3) dimensions without relying on a signal's phase.